Compare. 11sqrt (12)ldots 12sqrt (18)

To compare the two expressions \(11\sqrt{12}\) and \(12\sqrt{18}\), we can simplify them first.<br /><br />1. Simplify \(11\sqrt{12}\):<br />\[ 11\sqrt{12} = 11 \times \sqrt{4 \times 3} = 11 \times 2 \times \sqrt{3} = 22\sqrt{3} \]<br /><br />2. Simplify \(12\sqrt{18}\):<br />\[ 12\sqrt{18} = 12 \times \sqrt{9 \times 2} = 12 \times 3 \times \sqrt{2} = 36\sqrt{2} \]<br /><br />Now we need to compare \(22\sqrt{3}\) and \(36\sqrt{2}\).<br /><br />To do this, we can approximate the values of \(\sqrt{3}\) and \(\sqrt{2}\):<br />\[ \sqrt{3} \approx 1.732 \]<br />\[ \sqrt{2} \approx 1.414 \]<br /><br />Now substitute these approximations back into the expressions:<br />\[ 22\sqrt{3} \approx 22 \times 1.732 = 38.104 \]<br />\[ 36\sqrt{2} \approx 36 \times 1.414 = 50.904 \]<br /><br />Clearly, \(38.104 < 50.904\).<br /><br />Therefore, \(11\sqrt{12} < 12\sqrt{18}\).